The unified rule of phyllotaxis explaining both spiral and non-spiral arrangements

Contact pressure models for spiral phyllotaxis and their computer simulation.

We present a simple, biologically motivated model for the creation of phyllotactical patterns in capitula and their computer simulation. An in-depth investigation of Ridley's contact pressure model is performed and a refinement of contact pressure between primordia on the basis of local centroidal Voronoi relaxation is presented. Using this method in combination with Hofmeisters rule for placin...

A Unified Scaling Law in Spiral Galaxies.

We investigate the origin of a unified scaling relation in spiral galaxies. Observed spiral galaxies are spread on a plane in the three-dimensional logarithmic space of luminosity L, radius R, and rotation velocity V. The plane is expressed as L~&parl0;VR&parr0;alpha in the I passband, where alpha is a constant. On the plane, observed galaxies are distributed in an elongated region which looks ...

Spiral length design

On the circular curve, lateral acceleration affects comfort. On the spiral, both lateral acceleration and jerk affect comfort.  The determination of maximum curving speed on the basis of lateral acceleration only is not critical because the lateral acceleration is proportional to the square of speed whereas jerk is proportional to cubic power of speed. The maximum speed on a curve is thus signi...

Phyllotaxis or the properties of spiral lattices. - II. Packing of circles along logarithmic spirals

Phyllotaxis, or the properties of spiral lattices. - I. Shape invariance under compression